Let's investigate the average salary of four teams:

• Los Angeles Dodgers
• New York Yankees
• Tampa Bay Devil Rays
• Arizona Diamondbacks

url <- "http://www.usatoday.com/sports/mlb/salaries/"
salaries <- read_csv("mlb_salaries.csv") %>%
  select(NAME, TEAM, POS, SALARY)
salaries_trim <- salaries %>% 
  filter(TEAM %in% c("LAD", "NYY", "TB", "ARI"))
salaries_summary <- salaries_trim %>% group_by(TEAM) %>%
  summarize(mean_sal = mean(SALARY), count_team = n())
grand_mean <- salaries %>% summarize(mean(SALARY))

• 120 player salaries available for those four teams

• The mean salary for ALL 120 players on those four teams is \[\mu = \$4,214,614\]

• Remember, this is a summary value for the population. We hardly ever have the whole population to work with.

n <- 40
set.seed(20160129)
mean_srs <- salaries %>% 
  sample_n(n) %>%
  summarize(mean_srs_salary = mean(SALARY))

• Suppose we select 40 players at random from the 120 total

• \(\bar{x}_{SRS} = \$4,248,380\)

strat_n <- 10
mean_strat_by_team <- salaries %>% group_by(TEAM) %>%
  sample_n(strat_n) %>%
  summarize(mean_by_team = mean(SALARY))
mean_strat <- mean_strat_by_team %>%
  summarize(mean(mean_by_team))

• Let's select 10 players from each of the 4 teams

• \(\bar{x}_{STRAT} = \$3,998,016\)

• SRS: Absolute bias of $33,766.27

• Stratified: Absolute bias of $216,597.9

So is this evidence that simple random sampling is clearly better?

1. Find your numerical pair
2. Introduce yourself (name, year, major, hometown)
3. Discuss the problems on the handout and record your thoughts.